First principles calculations of magneto-crystalline anisotropy of rare-earth magnets

Abstract Magneto-crystalline anisotropies, K u , and anisotropic magnetic fields, H a , of two rare-earth (RE) magnets, i.e. CeFe 12 , and PrFe 12 , are theoretically calculated by using the crystal field (CF) method based on the first principles density functional theory (DFT) and the non-collinear DFT + U (NCDFT + U) method. The CF method reproduces an experimental H a of PrFe 12 but it failed to reproduce the H a of CeFe 12 , providing H a with a wrong sign. The NCDFT + U method correctly reproduces experimental H a of CeFe 12 and PrFe 12 , however the optimization of effective Hubbard on-site interaction parameters, U eff , of the 4 f electrons of the magnets is indispensable for the accurate calculation of H a . We have found that the CF method is valid in so far as it is used for the study of K u of RE magnets, which have RE atoms heavier than Pr atom. We expect that the NCDFT + U method would become a quantitative K u calculation method of any RE magnets if the U eff calculation method of 4 f electrons of RE magnets is established.